Summarize values per row using field calculator via Model Builder

I would go the route of using cursors. I'm not sure of the field names that you are using, but something like this should work assuming that the VSG_EINZEL fields are numerical:

import arcpy
# use workspace env or give an absolute path for fc
arcpy.env.workspace = "workspace"
fc = "feature_class"

# making a list of fields that contain VSG_EIZEL
# ex VSG_EINZEL, VSG_EIZEL_1, VSG_EIZEL_2
field_prefix = "VSG_EINZEL"
field_list = []
f_list = arcpy.ListFields(fc)
for f in f_list:
    if field_prefix in f.name:
        field_list.append(f.name)

# use update cursor to find values
# and update the total field
rows = arcpy.UpdateCursor(fc)
for row in rows:
    VSG_SUM = 0
    for f in field_list:
        VSG_SUM += row.getValue(f)
    row.VSG_ALL = VSG_SUM
    rows.updateRow(row)
    del VSG_SUM
del rows

It might need a little adjusting to fit your needs.

The Summary Statistics tool (in the Analysis Tools | Statistics toolbox) is probably what you're looking for. You can specify that particular field (VSG_EINZEL) and the statistic you want (SUM); it can work with however many values you have in VSG_EINZEL.

The output is a table, which may not be ideal for further calculations -- but hopefully this at least gets you further along. (If you want to do this in Python rather than via Arc tools, the approach would be different, but you could get a numerical value rather than a table.)

edited to add: For a fully-Python approach, the suggestions here may be useful.

I think I did something like this once (not with model builder), I just added a new field and created a sum of the attributes I was interested in; then I used the summarize function to get a table about my results. In my case, I was after minimum and maximum values as well as the sum so I needed three new fields (and I think I had all kinds of headaches because I didn't even think about the possibility of a tie in the data).